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In this work, we classify all the possible local four-point couplingsrelevant for tree-level flat space $2 \rightarrow 2$ scattering of externalmassive particles of spin one and spin two which do not grow faster than $s^2$at large $s$ and fixed t. This kinematic constraint on local growth oftree-level S-matrices is known as Classical Regge Growth criteria or CRG. Wefirst construct the spin one and spin two tree-level contact S-matrices asmodules of polarisation tensors and momenta over the ring of polynomialsgenerated by Mandelstam invariants. We then consider a general scatteringprocess where the external scattering particles are of different masses but ofsame spin and constrain this space to obtain a finite number of CRG allowedlocal Lagrangians. Our concrete results are primarily for $D\geq 8$ but theprocess outlined is easily generalised to lower dimensions to include lowdimensional parity violating structures. The space of CRG allowed structuresreduces when we specialise to identical scattering and restrict to parity evencouplings in $D=4$. We show that tree-level scattering amplitudes involvingexchange diagrams and contact terms in de Rham-Gabadadze-Tolley massive gravity(dRGT) violate CRG unless the parameters of the theory take special values. TheCRG allowed S-matrices, in the context of large $N$ conformal field theories(CFTs), can also be interpreted as bulk $AdS$ counterterms consistent withChaos bound. Our classified structures therefore can be thought of asambiguities arising in the context of conformal field theory inversion formulafor four point functions of unconserved spin one and spin two operators inlarge $N$ CFTs.

Regge constraints on local four-point scattering amplitudes of massive particles with spin